Department of Mathematics

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Author: search.filters.author.Dr. Hani Shaker, Assistant Profesor [Supervisor]Subject: search.filters.subject.department of mathematics

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    Topological In Variants Of Graphs
    (Library Information Services, COMSATS University, Lahore Campus, 2017) Imran Nadeem,; FA13-PMATH-003; Dr. Hani Shaker, Assistant Profesor [Supervisor]
    Chemical graph theory provides useful tools such as molecular descriptors to develop strong intrinsic relationship between the physicochemical features of chemical com pounds and their molecular graphs. The study of molecular descriptors provides a the oretical basis for the fabrication of chemical materials and is helpful in making up for the lack of chemical experiments. There are two prominent types of molecular descrip tors; the topological indices and counting polynomials. Further, topological indices can be categorized in two major classes: one class is based on degree and the other class is based on distance. In this thesis, we present the study of certain topological indices belonging to degree- and distance-based classes and counting polynomials for some well-known nanostructures. We also present a comparative study between dif ferent topological indices belonging to degree- and distance-based classes for general graphs. In addition, we study the para-line transformation of graphs and obtain the gen eral expressions of certain topological indices for this transformation. We achieve the lower and upper bounds of certain distance-based topological indices for the para-line transformation of graphs
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    On Algebraic Aspects Of Spanning Complexes
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Asif Allah Ditta,; FA17-RMT-027 Contributor(s):; Dr. Hani Shaker, Assistant Profesor [Supervisor]; LHR TP 5656
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    Merrifield-Simmons Index Of Molecular Graphs
    (COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2018) Noor-Un-Nisa,; FA16-RMT-014; Dr. Hani Shaker, Assistant Profesor [Supervisor]; LHR TP 5185
    The mainobjective of this thesis is to compute Merrifield- Simmons index of molecular graphs. The molecular graph that is taken for this purpose is V- phenlynic graph. The nanostructures under consideration are nanosheet G = V PHY[p,q] and H = VPHZ[p,q] nanotube. We compute the results for V- phenlynic nanosheet and nano tube. To compute Merrifield- Simmons index, first we find all independent sets of said graphs. We use the technique of transfer matrix to solve this problem. We develop some algorithms to compute Merrifield- Simmons index of said graphs. We construct a matlab program for the final results.